hyperdirichlet (version 1.5-1)

pollen:

Description

Data from Mosimann 1962 detailing forest pollen counts

Usage

data(pollen)

Format

A matrix with four columns and 76 rows.

Details

The rows each sum to 100; the values are counts of four different types of pollen. Each row corresponds to a different level in the core; the levels are in sequence with the first row being most recent and the last row being the oldest.

References

J. E. Mosimann 1962. “On the compound multinomial distribution, the multivariate \(\beta\)-distribution, and correlations among proportions”. Biometrika, volume 49, numbers 1 and 2, pp65-82.

See Also

serum

Examples

data(pollen)

func <- function(x,l){
ifelse(any(l<0),Inf,
 lfactorial(sum(x)) -sum(lfactorial(x))
    +lgamma(sum(l)) +sum(lgamma  (x+l))
    -sum(lgamma(l)) -lgamma(sum  (x+l))
)
}

start_vec <- c(51.6, 1, 5.3 , 2)

optim(start_vec , function(l){ -sum(apply(pollen , 1, FUN=func,l=l))})